Redshift distortions in one-dimensional power spectra

Abstract

We present a model for one-dimensional (ID) matter power spectra in redshift space as estimated from data provided along individual lines of sight. We derive analytic expressions for these power spectra in the linear and non-linear regimes, focusing on redshift distortions arising from peculiar velocities. In the linear regime, redshift distortions enhance the ID power spectra only on small scales and do not affect the power on large scales. This is in contrast to the effect of distortions on three-dimensional (3D) power spectra estimated from data in 3D space, where the enhancement is independent of scale. For cold dark matter (CDM) cosmologies, the ID power spectra in redshift and real space are similar for wavenumbers q ≲ 0.1 h Mpc-1 where both have a spectral index close to unity, independent of the details of the 3D power spectrum. Non-linear corrections drive the ID power spectrum in redshift space into a nearly universal shape over scales q ≲ 10 h Mpc -1, and suppress the power on small scales as a result of the strong velocity shear and random motions. The redshift-space ID power spectrum is mostly sensitive to the amplitude of the initial density perturbations. Our results are useful in particular for power spectra computed from the Sloan Digital Sky Survey (SDSS) quasars sample.